Question

if angle b measures 25°, what is the approximate perimeter of the triangle below?
10.3 units
11.8 units
22.1 units
25.2 units

Explanation:

Step1: Find side AC (opposite ∠B)

Use tangent function: $\tan(\theta)=\frac{\text{opposite}}{\text{adjacent}}$
$\tan(25^\circ)=\frac{AC}{4}$
$AC = 4\times\tan(25^\circ)\approx4\times0.4663=1.8652$

Step2: Find side BC (hypotenuse)

Use cosine function: $\cos(\theta)=\frac{\text{adjacent}}{\text{hypotenuse}}$
$\cos(25^\circ)=\frac{4}{BC}$
$BC=\frac{4}{\cos(25^\circ)}\approx\frac{4}{0.9063}=4.4135$

Step3: Calculate perimeter

Sum all sides: $AB + AC + BC$
$Perimeter\approx4 + 1.8652 + 4.4135$

Answer:

10.3 units